It certainly would have been nice if Jesus bothered to write things down but he couldn't or didn't want to.
It would have been nice if a couple of his followers wrote stuff down. But apparently they couldn't or didn't want to.
Now my limited understanding is that just about every village had a scribe back in those days. So it wouldn't have been that difficult to copy down the high lights of what Jesus thought and taught.
What we do know is we have an oral history told in many different languages as Christianity was spread along the Roman trade routes.
And maybe that is the key to the success of Christianity. And why it really hasn't been necessary to prove that Jesus lived.
This became an adaptable religion. Differences in language weren't a problem. Difference in culture and traditions could be accommodated as people could find a way forward in the simple words of someone called Jesus.
I don't think this was the master plan. The Jesus of the Bible was Israel centric,and anti the religious leaders of his day. He was also violent at times.
What Jesus became accountable for was the opportunity to take his simple words and teachings and blend them into whatever nation or state needed to find a new way of looking at things.
Take Greece......the old gods were dying off, the philosophy of the Greek teachers was not always applicable.
The Jewish religion was welcomed in Greece and it paved the way for Christianity.
To this day Christianity adapts and grows.....as a movement it does not really matter if Jesus was real or not since no one wrote anything down when he lived.....maybe what we are left with are the best intentions of a made up character.